In the present study, we will restrict ourselves to the situation in which both liquid phases are dragged, giving birth to a superposition of two liquid films on the substrate.
It is worth mentioning the connection of this configuration to the model introduced by [1]} to describe the dip-coating of a textured solid with a single liquid phase.
In that work, the effect of the texture was modelled as a secondary, uniform layer made of a fluid with a viscosity higher than that of the coating liquid.
Finally, in a different geometry, the entrainment of a thin liquid film at a liquid/liquid interface has been described in the context of lubricant-infused surfaces [2]}.
When a water droplet is sliding on an oil-imbibed surface, thin oil films observed behind, beneath or around the droplet have been shown to obey similar scaling laws as in the LLD theory [3]}, [4]}.
